Study of the Bacterial "Conversations" and Pattern Formation in the Quorum Sensing System using Numerical Simulation

Sarangam Majumdar, Sisir Roy, Rodolfo R. Llinás

Abstract


Cell-to-cell communication processes in the bacterial world can be considered as a collective bacterial behavior, which is coordinated by chemical signaling molecules (autoinducers, quorum sensing molecules, or pheromones). This complex biological process is termed the quorum sensing mechanism, which is considered a density-dependent bacterial communication system. As the bacterial culture grows, signal molecules are released into the extracellular milieu and accumulate, changing water fluidity. Under such threshold conditions, swimming bacterial suspensions impose a coordinated water movement on a length scale of the order of 10 to 100 micrometers compared with a bacterial size of the order of 3 micrometers. Here, we propose a non-local hydrodynamics of the quorum state and wave-like pattern formation using the forced Burgers equation with Kwak transformation. Such an approach resulted in the conversion of the Burgers equation paradigm into a reaction-diffusion system. The examination of the dynamics of the quorum sensing system, both analytically as well as numerically, results in similar long-time dynamical behaviour. Moreover, we find out the range kinematics viscosity of the living fluid, which is one of the significant parameters for pattern formation in the system.

AMS Subject Classification: 92B05, 65N06, 65Z05.

 

Doi: 10.28991/HEF-SP2022-01-03

Full Text: PDF


Keywords


Quorum Sensing; Non-local Hydrodynamics; Pattern Formation; Reaction-diffusion Equation; Kwak Transformation; Forced Burger Equation; Kinematic Viscosity.

References


Lopez, D., & Lauga, E. (2014). Dynamics of swimming bacteria at complex interfaces. Physics of Fluids, 26(7), 071902. doi:10.1063/1.4887255.

Long, T., Tu, K. C., Wang, Y., Mehta, P., Ong, N. P., Bassler, B. L., & Wingreen, N. S. (2009). Quantifying the Integration of Quorum-Sensing Signals with Single-Cell Resolution. PLoS Biology, 7(3), e1000068. doi:10.1371/journal.pbio.1000068.

Miller, M. B., & Bassler, B. L. (2001). Quorum Sensing in Bacteria. Annual Review of Microbiology, 55(1), 165–199. doi:10.1146/annurev.micro.55.1.165.

Waters, C. M., & Bassler, B. L. (2005). Quorum Sensing: Cell-to-Cell Communication in Bacteria. Annual Review of Cell and Developmental Biology, 21(1), 319–346. doi:10.1146/annurev.cellbio.21.012704.131001.

Williams, P., Winzer, K., Chan, W. C., & Camara, M. (2007). Look who's talking: communication and quorum sensing in the bacterial world. Philosophical Transactions of the Royal Society B: Biological Sciences, 362(1483), 1119-1134. doi:10.1098/rstb.2007.2039.

Qazi, S. N. A., Counil, E., Morrissey, J., Rees, C. E. D., Cockayne, A., Winzer, K., … Hill, P. J. (2001). Agr Expression Precedes Escape of Internalized Staphylococcus aureus from the Host Endosome. Infection and Immunity, 69(11), 7074–7082. doi:10.1128/iai.69.11.7074-7082.2001.

Withers, H., Swift, S., & Williams, P. (2001). Quorum sensing as an integral component of gene regulatory networks in Gram-negative bacteria. Current opinion in microbiology, 4(2), 186-193. doi:10.1016/S1369-5274(00)00187-9.

Majumdar, S., & Mondal, S. (2016). Conversation game: talking bacteria. Journal of Cell Communication and Signaling, 10(4), 331–335. doi:10.1007/s12079-016-0333-y.

Roy, Sisir, and Rodolfo Llinas. (2016). "Non-local hydrodynamics of swimming bacteria and self-activated process.", Biomat 2015 Proceedings of the International Symposium on Mathematical and Computational Biology. World Scientific: 153-165. doi:10.1142/9789813141919_0010

Bateman, H. (1915). Some recent researches on the motion of fluids. Monthly Weather Review, 43(4), 163-170.

Burgers, J. M. (1948). A Mathematical Model Illustrating the Theory of Turbulence. Advances in Applied Mechanics Volume 1, 171–199. doi:10.1016/s0065-2156(08)70100-5.

Burgers, J. M. (2013). The nonlinear diffusion equation: asymptotic solutions and statistical problems. Springer Science & Business Media, Berlin, Germany.

Hopf, E. (1950). The partial differential equation ut + uux = μxx. Communications on Pure and Applied Mathematics, 3(3), 201–230. doi:10.1002/cpa.3160030302.

Kwak, M. (1992). Finite-dimensional description of convective Reaction-Diffusion equations. Journal of Dynamics and Differential Equations, 4(3), 515–543. doi:10.1007/bf01053808.

Smaoui, N. (2000). Analyzing the dynamics of the forced Burgers equation. Journal of Applied Mathematics and Stochastic Analysis, 13(3), 269–285. doi:10.1155/s1048953300000241.

Berking, S. (1981). Zur Rolle von Modellen in der Entwicklungsbiologie. doi:10.1007/978-3-662-11001-0.

Basu, S., Gerchman, Y., Collins, C. H., Arnold, F. H., & Weiss, R. (2005). A synthetic multicellular system for programmed pattern formation. Nature, 434(7037), 1130–1134. doi:10.1038/nature03461.

Datla, U. S., Mather, W. H., Chen, S., Shoultz, I. W., Täuber, U. C., Jones, C. N., & Butzin, N. C. (2017). The spatiotemporal system dynamics of acquired resistance in an engineered microecology. Scientific Reports, 7(1). doi:10.1038/s41598-017-16176-w.

Kuttler, C., & Maslovskaya, A. (2021). Hybrid stochastic fractional-based approach to modeling bacterial quorum sensing. Applied Mathematical Modelling, 93, 360–375. doi:10.1016/j.apm.2020.12.019.

Monaco, H., Liu, K. S., Sereno, T., Deforet, M., Taylor, B. P., Chen, Y., … Xavier, J. B. (2022). Spatial-temporal dynamics of a microbial cooperative behavior resistant to cheating. Nature Communications, 13(1). doi:10.1038/s41467-022-28321-9.


Full Text: PDF

DOI: 10.28991/HEF-SP2022-01-03

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Sarangam Majumdar, Sisir Roy, Rodolfo Llinas